CN109617538A

CN109617538A - The sparse sef-adapting filter of the variable element of robust

Info

Publication number: CN109617538A
Application number: CN201811499655.2A
Authority: CN
Inventors: 倪锦根; 陈旭
Original assignee: Suzhou University
Current assignee: Suzhou University
Priority date: 2018-12-09
Filing date: 2018-12-09
Publication date: 2019-04-12
Anticipated expiration: 2038-12-09
Also published as: CN109617538B

Abstract

The invention discloses a kind of sparse sef-adapting filters of the variable element of robust, belong to digital filter design field.The filter mainly to accelerate the convergence rate of sef-adapting filter and reduces its steady output rate using the regularization parameter of zero attractor intensity of time change step length parameter and control.The sparse sef-adapting filter of the variable element of robust disclosed by the invention inputs for white signal in input and in the influence for having impulsive noise, and performance has better constringency performance compared with conventional symbols filter.The sparse sef-adapting filter of the variable element of robust disclosed by the invention can be applied to the fields such as the electronics of echo cancellor, noise eliminator, signal enhancing and disturbing pulse, communication equipment.

Description

The sparse sef-adapting filter of the variable element of robust

Technical field

The invention discloses a kind of sparse sef-adapting filters of the variable element of robust, belong to digital filter design field.

Background technique

Traditional least-mean-square filter (LMS) and normalization minimum mean-square filter (NLMS) is in sef-adapting filter It has a wide range of applications, such as self-adaptive echo counteracting, active noise controlling and adaptation noise are eliminated.

Convergence rate, steady output rate and anti-impulse disturbances ability are three important performance indexes of sef-adapting filter.Surely The height of state imbalance determines that sef-adapting filter approaches the precision that unknown system can reach, and the speed of convergence rate determines Sef-adapting filter approaches the time that unknown system needs to spend, and anti-impulse disturbances ability determines the Shandong of sef-adapting filter Stick, these three indexs affect the quality of signal processing simultaneously.

When sef-adapting filter is by impulse noise interference, the stable state of these traditional LMS and NLMS sef-adapting filters Imbalance will increase, or even diverging.Using symbol LMS (the being denoted as SE-LMS) sef-adapting filter for taking symbolic operation to evaluated error [Sayed A H, Adaptive filters, John Wiley&Sons, 2008], can greatly reduce impulsive noise to adaptive Answer the influence of filter.However the SE-LMS sef-adapting filter of fixed step size, convergence rate and steady output rate cannot be simultaneously Obtain optimal value.

In order to further decrease the steady output rate of filter, adaptively filtered using the symbol LMS (being denoted as VSSA) of variable step Wave device [Yuan-Ping Li, Ta-Sung Lee, Bing-Fei Wu.A variable step-size sign algorithm For channel estimation, Signal Processing, 102:304-312], which can substantially reduce filtering The steady output rate of device.In addition, in some applications, the unknown system of sef-adapting filter estimation may be it is sparse, use SE- LMS or VSSA sef-adapting filter is unable to fully accelerate to restrain using its sparse characteristic.

In order to further speed up the convergence rate of filter, the present invention discloses a kind of sparse adaptive filter of variable element of robust Wave device, which, which uses, has l₀The variable element notation method (being denoted as VP-SE-LMS) of norm constraint is updated.This is adaptive Answering filter not only has stronger robustness, but also can improve the convergence rate of estimation Sparse System.It is disclosed by the invention adaptive Filter is answered to can be used for comprising in the electronic instruments and equipment of functions such as echo cancelltion, noise elimination, channel estimation.

Summary of the invention

The sparse sef-adapting filter of the variable element of robust disclosed by the invention, using the base in absolute value error cost function The method that a zero attractor bound term of arc tangent is added on plinth is established, and step parameter and regularization parameter are with the number of iterations Change and adjust automatically, to improve the performance of sef-adapting filter.

The principle of technical solution of the present invention is as follows:

A kind of sparse sef-adapting filter of the variable element of robust, updates its weight vector w_nSpecific step is as follows:

1) by input signal vector x_nWith the weight vector w of sef-adapting filter_nInner product is carried out, sef-adapting filter is generated Output y_n, i.e.,Wherein: x_n=[x_n, x_n-1..., x_n-M+1]^T, and x_n, x_n-1..., x_n-M+1Indicate the n moment to n-M+ M sample value of 1 moment input signal；w_n=[w_{0, n}, w_{1, n}..., w_{M-1, n}]^T, and w_{0, n}, w_{1, n}..., w_{M-1, n}Indicate n moment weight Vector w_nM element；M is integer, and subscript T indicates transposition operation；

2) according to e_n=d_n-y_nCalculate the evaluated error e at n moment_n, in which: d_nIndicate the desired signal of unknown system；

3) according to ψ_n=median (| e_n|, | e_n-1| ..., | e_n-L+1|) calculate n moment to the n-L+1 moment evaluated error {|e_n|, | e_n-1| ..., | e_n-L+1| intermediate value ψ_n, wherein median () expression asks median operation to accord with, | | it indicates to scalar Or each element of vector carries out the operation that takes absolute value, L indicates the length of intermediate value window；

4) basisWithTo calculate the estimation of additional mean square error Value, whereinIndicate evaluated errorIn the smooth value at n moment, β is smoothing factor,For additional mean square error ζ_nEstimated value,For the minimum value of additional mean square error,For noise z_nVariance；

5) basis WithCalculate time change step length parameter The intermediate variable a needed with time-varying regularization parameter_n、b_n、c_n、p_1n、g_nAnd p_2n, in which: sgn { } is indicated to scalar or vector Each element carries out taking symbolic operation,Indicate that the element of former and later two vector corresponding positions of the operator is divided by respectively,It is defeated Enter signal x_nVariance；

6) basisCalculate the time change step length parameter of estimationAccording toCalculate the time-varying regularization parameter of estimation

7) by the time change step length parameter of estimationWith the time-varying regularization parameter of estimationIt is limited to nonnegative value, even

8) basisCalculate smoothed out time-varying step Long parameter μ_nWith smoothed out time-varying regularization parameter ρ_n, whereinFor smoothing factor, μ_maxFor the step parameter maximum value of permission；

9) basisCalculate the n+1 moment The outer mean square error of jot

10) formula is usedUpdate weight vector w_n。

Beneficial effect

Scheme in compared with the existing technology, the sparse sef-adapting filter of the variable element of robust disclosed by the invention maintain It is estimated preferably constringency performance when Sparse System and inhibits the interference of impulsive noise.

Detailed description of the invention

The invention will be further described with reference to the accompanying drawings and embodiments:

Fig. 1 is the sparse sef-adapting filter block diagram of variable element of robust；

Under the conditions of Fig. 2 is described in the embodiment, the normalization mean-squared departure of SE-LMS, VSSA and VP-SE-LMS filter Learning curve compares figure.

Specific embodiment

Embodiment

The present embodiment compares SE-LMS, VSSA sef-adapting filter by the method for computer-experiment and the present invention discloses VP-SE-LMS sef-adapting filter convergence rate and steady output rate.

One, experiment condition:

Experimental setup is as shown in Figure 1, input signal x_nFor the white Gaussian noise of zero-mean, variance isMeasurement is made an uproar Sound is by white Gaussian noise z_nWith impulsive noise θ_nSynthesis, wherein z_nVariance beImpulsive noise θ_nBy Bernoulli process τ_nWith Gaussian process t_nProduct generate, i.e. θ_n=t_nτ_n, and probability distribution meets P (τ_n=1)=0.01, P (τ_n=0)= 0.99.In MATLAB environment, the weight vector w of unknown system is generated_o=[0.8,0.5,0.3,0.2,0.1,0.05, zeros (1,36), -0.05, -0.1, -0.2, -0.3, -0.5, -0.8]^T。

Two, experimental procedures:

1. initialization:

w₁=[zeros (Isosorbide-5-Nitrae 8)]^T, ρ₀=0, μ₀=0.01, L=11,β= 0.997；

2. updating weight vector w by following each expression formula at the moment of n >=1_n:

1)

2)e_n=d_n-y_n；

3)ψ_n=median (| e_n|, | e_n-1| ..., | e_n-L+1|)；

4)

5)

6)

7)

8)

9)

10)

Three, experimental results:

Performance indicator, expression formula 20log are used as using the normalization mean-squared departure (NMSD) changed with the number of iterations₁₀ (||w_o-w_n||/||w_o| |), unit is decibel (dB).All NMSD curves are the result that 100 independent experiments are averaged.Such as Shown in Fig. 2, the weight vector of unknown system is estimated, VP-SE-LMS sef-adapting filter ratio SE- disclosed by the invention LMS sef-adapting filter has lower steady output rate, has faster convergence rate than VSSA sef-adapting filter.

The above embodiments merely illustrate the technical concept and features of the present invention, and its object is to allow person skilled in the art It cans understand the content of the present invention and implement it accordingly, it is not intended to limit the scope of the present invention.It is all smart according to the present invention The equivalent transformation or modification that refreshing essence is done, should be covered by the protection scope of the present invention.

Claims

1. a kind of sparse sef-adapting filter of the variable element of robust, it is characterised in that: the sef-adapting filter uses variable step Parameter updates sef-adapting filter weight vector with the change regularization parameter for controlling zero attractor intensity.

2. the sparse sef-adapting filter of the variable element of robust according to claim 1, it is characterised in that: the adaptive filter Wave device estimates the step-size parameter mu at n moment using following steps_nWith regularization parameter ρ_n

1) by input signal vector x_nWith the weight vector w of sef-adapting filter_nInner product is carried out, the defeated of sef-adapting filter is generated Y out_n, i.e.,Wherein: x_n=[x_n, x_n-1..., x_n-M+1]^T, and x_n, x_n-1..., x_n-M+1When indicating that the n moment is to n-M+1 Carve M sample value of input signal；w_n=[w_{0, n}, w_{1, n}..., w_{M-1, n}]^T, and w_{0, n}, w_{1, n}..., w_{M-1, n}Indicate n moment weight vector w_nM element；M is integer, and subscript T indicates transposition operation；

2) according to e_n=d_n-y_nCalculate the evaluated error e at n moment_n, wherein d_nIndicate the desired signal of unknown system；

3) according to ψ_n=median (| e_n|, | e_n-1| ..., | e_n-L+1|) calculate n moment to the n-L+1 moment evaluated error | e_n|, |e_n-1| ..., | e_n-L+1| intermediate value ψ_n, wherein median () expression asks median operation to accord with, | | it indicates to scalar or vector Each element carry out the operation that takes absolute value, L indicates the length of intermediate value window；

4) basisWithCalculate the estimated value of additional mean square error, InIndicate evaluated errorIn the smooth value at n moment, β is smoothing factor,For additional mean square error ζ_nEstimated value, For the minimum value of additional mean square error,For without impulsive noise z_nVariance；

6) basisCalculate the time change step length parameter of estimationAnd according toCalculate the time-varying regularization parameter of estimation

8) basisCalculate smoothed out time change step length ginseng Number μ_nWith smoothed out time-varying regularization parameter ρ_n, whereinFor smoothing factor, μ_maxFor the step parameter maximum value of permission；

9) basisCalculate the n+1 moment most Small additional mean square error

3. the sparse sef-adapting filter of the variable element of robust according to claim 2, it is characterised in that: the adaptive filter Wave device uses calculating formulaUpdate weight vector w_n。